Hardware Implementation of Floating-Point Arithmetic

Muller, Jean-Michel; Brunie, Nicolas; Dinechin, Florent de; Jeannerod, Claude-Pierre; Joldeş, Mioara; Lefèvre, Vincent; Melquiond, Guillaume; Revol, Nathalie; Torres, Serge

doi:10.1007/978-3-319-76526-6_8

Cited by 5 publications

(3 citation statements)

References 142 publications

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“…Floating-point arithmetic has became widely used in many applications such as 3D graphics, scientific computing and signal processing [1][2][3][4][5], implemented both in hardware and software [6][7][8][9][10]. Many algorithms can be used to approximate elementary functions [1,2,[10][11][12][13][14][15][16][17][18].…”

Section: Introductionmentioning

confidence: 99%

A Modification of the Fast Inverse Square Root Algorithm

2019

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We present a new algorithm for the approximate evaluation of the inverse square root for single-precision floating-point numbers. This is a modification of the famous fast inverse square root code. We use the same “magic constant” to compute the seed solution, but then, we apply Newton–Raphson corrections with modified coefficients. As compared to the original fast inverse square root code, the new algorithm is two-times more accurate in the case of one Newton–Raphson correction and almost seven-times more accurate in the case of two corrections. We discuss relative errors within our analytical approach and perform numerical tests of our algorithm for all numbers of the type float.

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Section: Introductionmentioning

confidence: 99%

A Modification of the Fast Inverse Square Root Algorithm

2019

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“…Floating-point arithmetics has became wide spread in many applications such as 3D graphics, scientific computing and signal processing [1,2,3]. Basic operators such as addition, subtraction, multiplication are easier to design and yield higher performance, high throughput but advanced operators such as division, square root, inverse square root and trigonometric functions consume more hardware, slower in performance and slower throughput [4,5,6,7,8].…”

Section: Introductionmentioning

confidence: 99%

Fast calculation of inverse square root with the use of magic constant – analytical approach

Moroz

Walczyk

Hrynchyshyn

et al. 2018

Applied Mathematics and Computation

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“…Floating-point arithmetic has became widely used in many applications such as 3D graphics, scientific computing and signal processing [1,2,3,4,5], implemented both in hardware and software [6,7,8,9,10]. Many algorithms can be used to approximate elementary functions, including the inverse square root [1,2,10,11,12,13,14,15,16,17,18,19].…”

Section: Introductionmentioning

confidence: 99%

A Modification of the Fast Inverse Square Root Algorithm

Walczyk¹,

Moroz²,

Cieśliński³

2019

Preprint

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We present improved algorithms for fast calculation of the inverse square root for single-precision floating-point numbers. The algorithms are much more accurate than the famous fast inverse square root algorithm and have the same or similar computational cost. The main idea of our work consists in modifying the Newton-Raphson method and demanding that the maximal error is as small as possible. The modification can be applied when the distribution of Newton-Raphson corrections is not symmetric (e.g., if they are non-positive functions).

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Hardware Implementation of Floating-Point Arithmetic

Cited by 5 publications

References 142 publications

A Modification of the Fast Inverse Square Root Algorithm

A Modification of the Fast Inverse Square Root Algorithm

Fast calculation of inverse square root with the use of magic constant – analytical approach

A Modification of the Fast Inverse Square Root Algorithm

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